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It is a fact stated as an exercise in chapter 9 of Lee's book "Riemannian Geometry" that any compact 2D manifold can be triangulated by geodesic triangles. Can one triangulate any compact Riemannian m …

$\DeclareMathOperator\dom{dom}$Sorry to bother the community again with these type of questions about power series, I am ready to delete the question if it is not suitable. Definition: I say a functio …

Let $R<S$ be an extension of commutative rings with identities (i.e. $R$ is a subring of $S$). We say $s_1,s_2,...,s_k$ are algebraically independent over $R$ iff there is no polynomial $f\in R[x_1,. …

Let $F\subseteq E$ be an algebraic field extension. Let $\alpha\in E$ be such that $\min(\alpha,F)$ has only one root in $E$ (which will be $\alpha$). Is it true that for any $p(x)\in F[x]$ we must ha …

I apologize in advance if this is a naive question. Def: A topological chain complex is a chain complex of topological $\mathbb{R}$-vector spaces such that the boundary maps are continuous. Let $C$ …

Let $f:M\rightarrow N$ be a smooth map between two simply connected Riemannian manifolds of the same dimension. It is also given that for every $x\in M$ we have that $Df|_x:T_xM\rightarrow T_{f(x)}N$ …

The following question arised in my research, and I was unable to settle it after playing with it for sometime. Let $\{a^k_i\}_{i\geq 1}$ (for $k\in \{1,2,3,4\}$) be four sequences of real numbers. F …